Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity

TL;DR

The paper develops a covariant formalism for deriving conservation laws and quantities for perturbations in general metric theories of gravity, unifying various approaches and validating with black hole mass calculations.

Contribution

It introduces a new family of conserved currents and superpotentials for perturbations in arbitrary metric theories, enhancing the understanding of conserved quantities in gravity.

Findings

Successfully calculates black hole mass using the new superpotentials.

Unifies different conserved quantities into a single covariant framework.

Validates the formalism with Einstein-Gauss-Bonnet gravity.

Abstract

A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized Noether identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical Noether and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein-Gauss-Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.